Comparing point patterns
This exercise will introduce functions found in the Geostatistical Analyst toolbar.
Introduction
The lab is organized around the following question in the Callalli data:
We know that obsidian is found about 15 km to the southwest of the area, but that chert cobbles are found in the local geology and the cobbles can be found in streambeds. We noted during fieldwork that chert artifacts are commonly found along the banks of the streams where there appeared to have been chert tool manufacture occurring. Obsidian appeared to be primarily located in discrete deposits that were imported from the source region.
On the principal of least effort we might expect that larger artifacts, particularly cores and concentrations of flakes, would be encountered close to the rivers in the case of chert but not in the case of obsidian. We could structure this in terms of hypothesis testing (H0: no relationships between weight of artifacts and proximity to streams; H1: concentrations of heavy chert artifacts are found in proximity to streams). However, a visual exploration of the relationship is also informative.
The Lithics_Lab2_All_ArchID table is constructed the same way as we created the Ceram_Lab2_All_ArchID last week. It is a de-normalized table where points were created for every artifact from our lab analysis using the best spatial provenience available.
Note that there are 390 artifact rows.
Look at the Attribute Table and observe the types of data involved. We have projectile points and other lithic tools, and a small sample of flakes. It turns out these flakes are only from a couple of sites, so lets exclude them. Also, we only want to work with Chert and Obsidian, so first we will select out the Chert non flakes using the Definition Query.
Your query should look something like
("Lit_Mat" = 'Chert' AND "Form" <> 'Flake Complete') and ("Lit_Mat" = 'Chert' AND "Form" <> 'Flake Broken')
Build it yourself so you remember how… don't just copy that text!
Note that we can now work with subsets of that single table without altering the original table. How many records are found in each Attribute Table?
B. Spatially explore the table values by Frequency.
First, turn on the Geostatistical Analyst. This takes two steps
We have Coinciding Samples… Choose “Include All”.
Why do we have spatially coinciding samples?
Note that you can interactively select by
- spatial position in the map (using the blue selection arrow)
- attribute characteristics from the table
- frequency (histogram) of values in Explore window
This tool is very useful for data exploration and pattern recognition.
This display also allows you to include histograms as well as values like Count, Mean, St. Dev., etc. on your map layout (using the Add to Layout button) where you can also export them to PDF for use in Word documents, etc.
Apply the Cluster/Outlier Analysis function that we used in lab last week
Input Feature: Chert Tools…
Input Field: Wt_g10
Output Layer File (click the Folder and name it: ChertWtLyr1)
Output Feature Class (click the Folder and name it: ChertWt1)
Look at the patterns. Zoom and and investigate the red and blue dots. These are features with statistically significant autocorrelation (positive or negative).
The values are Z scores which means that the numbers reflect standard deviations. For example, at a 95% confidence level you cannot reject the null hypothesis (of random distribution) unless the Z scores are in excess of +/- 1.96 (1 stan dev).
Look at those values in the Histogram and in the Attribute table. Can you figure out why they have high/low spatial autocorrelation values?
The Geostatistical Analyst provides tools for examining these kinds of patterns in detail.
In this brief introduction we will simply produce an IDW surface using the default values and compare it visually to the known patterns.
We don't have time to explore all the feature here, but this window is concerned with the directionality and magnitude of the interpolation.
This window displays the interpolation algorithm and allows you to reject specific interpolated (predicted) values that diverge from the Measured values.
Study the results. Compare the Clusters/Outliers results (red/blue dots) with the geostatistical wizard output.
It is somewhat difficult to compare the concentrations of heavy chert and obsidian artifacts from these rasters because they obscure each other.
You can compare the prediction strength in both layers
There are other powerful interpolation tools in the Geostatistical Analyst including kriging and semivariogram production. If you choose to use these methods you should research the most appropriate interpolator for your task.
The Subset function is also quite powerful in Geostatistical Analyst. It allows you to set aside a portion of your data for validation purposes. We will use this function in the coming weeks in the locational modeling exercise.